Question: Simplify the following expression: $ k = \dfrac{4q - 1}{-4q} + \dfrac{9}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{4q - 1}{-4q} \times \dfrac{7}{7} = \dfrac{28q - 7}{-28q} $ Multiply the second expression by $\dfrac{-4q}{-4q}$ $ \dfrac{9}{7} \times \dfrac{-4q}{-4q} = \dfrac{-36q}{-28q} $ Therefore $ k = \dfrac{28q - 7}{-28q} + \dfrac{-36q}{-28q} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{28q - 7 - 36q}{-28q} $ $k = \dfrac{-8q - 7}{-28q}$ Simplify the expression by dividing the numerator and denominator by -1: $k = \dfrac{8q + 7}{28q}$